A numerical experiment using direct numerical simulation (DNS) of the particular Couette-Poiseuille (C-P) flow in which the pressure gradient dP/dx is adjusted to create zero mean skin friction on the stationary wall is conducted. The quadrant analysis of the Reynolds stress is performed based on data from the DNS with emphasis on the structures near the frictionless wall. Reynolds structures are motions of the Reynolds stress u0v0 and their structure is investigated by quadrant analysis which splits the values of Reynolds stress into four quadrants (Qs). A fully resolved case with Reynolds number equal to 2880 is used. The Reynolds number Re is defined using the velocity of the moving wall uwall, viscosity ν and the half channel height h. Statistical and geometric characters of the Qs structures are investigated and reported.